Quantum Control of Cold Atoms using microwaves

Projecte final de Màster Oficial fet en col.laboració amb Universitat Autònoma de Barcelona (UAB), Universitat de Barcelona (UB)i Institut de Ciències Fotòniques (ICFO)English: We study quantum control of the ground hyperfine manifold of alkali-metal atoms based on applied microwave fields. We performed microwave spectroscopy both in the frequency and the time domain resulting in the observation of spectra and Rabi oscillations. We also apply a spin echo technique to characterize the coherence time of our trapped atoms.Castellà: En este proyecto estudiamos el control cuántico del estado fundamental de átomos alcalinos bajo la aplicación de campos de microondas. Se realiza espectroscopía de microondas tanto en la frecuencia como en tiempo resultante en la observación de los espectros y de oscilaciones de Rabi. También aplicamos una variante de la técnica de eco de spin para caracterizar el tiempo de la coherencia de nuestros átomos atrapados.Català: En aquest projecte estudiem el control quàntic de l'estat fonamental d'àtoms alcalins sota l'aplicació de camps de microones. Es realitzar espectroscòpia de microones tant en la freqüència com en temps resultant en l'observació dels espectres i d'oscil·lacions de Rabi. També apliquem una variant de la tècnica d'eco d'spin per caracteritzar el temps de la coherència dels nostres àtoms atrapats

Interferometric measurement of interhyperfine scattering lengths in 87^{87}Rb

We present interferometeric measurements of the $f=1$ to $f=2$ inter-hyperfine scattering lengths in a single-domain spinor Bose-Einstein condensate of $^{87}$Rb. The inter-hyperfine interaction leads to a strong and state-dependent modification of the spin-mixing dynamics with respect to a non-interacting description. We employ hyperfine-specific Faraday-rotation probing to reveal the evolution of the transverse magnetization in each hyperfine manifold for different state preparations, and a comagnetometer strategy to cancel laboratory magnetic noise. The method allows precise determination of inter-hyperfine scattering length differences, calibrated to intra-hyperfine scattering length differences. We report $(a_{3}^{(12)}-a_{2}^{(12)})/(a_{2}^{(1)}-a_{0}^{(1)})=-1.27(15)$ and $(a_{1}^{(12)}-a_{2}^{(12)})/(a_{2}^{(1)}-a_{0}^{(1)})=-1.31(13)$, limited by atom number uncertainty. With achievable control of atom number, we estimate precisions of $\approx 0.3\%$ should be possible with this technique

Bose-Einstein Condensate Comagnetometer

We describe a comagnetometer employing the $f=1$ and $f=2$ ground state hyperfine manifolds of a $^{87}$Rb spinor Bose-Einstein condensate as co-located magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The $f=1$ and $f=2$ transverse magnetizations and azimuth angles are independently measured by non-destructive Faraday rotation probing, and we demonstrate a $44.0(8)\text{dB}$ common-mode rejection in good agreement with theory. We show how spin-dependent interactions can be used to inhibit $2\rightarrow 1$ hyperfine relaxing collisions, extending to $\sim 1\text{s}$ the transverse spin lifetime of the $f=1,2$ mixtures. The technique could be used in high sensitivity searches for new physics on sub-millimeter length scales, precision studies of ultra-cold collision physics, and angle-resolved studies of quantum spin dynamics

The Multivariate Extension of the Lomb-Scargle Method

The common methods of spectral analysis for multivariate (n-dimensional) time series, like discrete Frourier transform (FT) or Wavelet transform, are based on Fourier series to decompose discrete data into a set of trigonometric model components, e. g. amplitude and phase. Applied to discrete data with a finite range several limitations of (time discrete) FT can be observed which are caused by the orthogonality mismatch of the trigonometric basis functions on a finite interval. However, in the general situation of non-equidistant or fragmented sampling FT based methods will cause significant errors in the parameter estimation. Therefore, the classical Lomb-Scargle method (LSM), which is not based on Fourier series, was developed as a statistical tool for one dimensional data to circumvent the inconsistent and erroneous parameter estimation of FT. The present work deduces LSM for n-dimensional data sets by a redefinition of the shifting parameter \tau, to maintain orthogonality of the trigonometric basis. An analytical derivation shows, that n-D LSM extents the traditional 1D case preserving all the statistical benefits, such as the improved noise rejection. Here, we derive the parameter confidence intervals for LSM and compare it with FT. Applications with ideal test data and experimental data will illustrate and support the proposed method.Comment: to be publishe

The Beauty of Symmetry: Common-mode rejection filters for high-speed interconnects and balanced microwave circuits

Common-mode rejection filters operating at microwave frequencies have been the subject of intensive research activity in the last decade. These filters are of interest for the suppression of common-mode noise in high-speed digital circuits, where differential signals are widely employed due to the high immunity to noise, electromagnetic interference (EMI) and crosstalk of differential-mode interconnects. These filters can also be used to improve common-mode rejection in microwave filters and circuits dealing with differential signals. Ideally, common-mode stopband filters should be transparent for the differential mode from DC up to very high frequencies (all-pass), should preserve the signal integrity for such mode, and should exhibit the widest and deepest possible rejection band for the common mode in the region of interest. Moreover, these characteristics should be achieved by means of structures with the smallest possible size. In this article, several techniques for the implementation of common-mode suppression filters in planar technology are reviewed. In all the cases, the strategy to simultaneously achieve common-mode suppression and all-pass behavior for the differential mode is based on selective mode-suppression. This selective mode suppression (either the common or the differential mode) in balanced lines is typically (although not exclusively) achieved by symmetrically loading the lines with symmetric resonant elements, opaque for the common-mode and transparent for the differential mode (common-mode suppression), or vice versa (differential-mode suppression).MINECO, Spain-TEC2013-40600-R, TEC2013-41913-PGeneralitat de Catalunya-2014SGR-15

Four-frequency solution in a magnetohydrodynamic Couette flow as a consequence of azimuthal symmetry breaking

The occurrence of magnetohydrodynamic (MHD) quasiperiodic flows with four fundamental frequencies in differentially rotating spherical geometry is understood in terms of a sequence of bifurcations breaking the azimuthal symmetry of the flow as the applied magnetic field strength is varied. These flows originate from unstable periodic and quasiperiodic states with broken equatorial symmetry but having four-fold azimuthal symmetry. A posterior bifurcation gives rise to two-fold symmetric quasiperiodic states, with three fundamental frequencies, and a further bifurcation to a four-frequency quasiperiodic state which has lost all the spatial symmetries. This bifurcation scenario may be favoured when differential rotation is increased and periodic flows with $m$-fold azimuthal symmetry, $m$ being product of several prime numbers, emerge at sufficiently large magnetic field.Comment: 8 pages, 7 figures, published in Phys. Rev. Le

Long term time dependent frequency analysis of chaotic waves in the weakly magnetized spherical Couette system

The long therm behavior of chaotic flows is investigated by means of time dependent frequency analysis. The system under test consists of an electrically conducting fluid, confined between two differentially rotating spheres. The spherical setup is exposed to an axial magnetic field. The classical Fourier Transform method provides a first estimation of the time dependence of the frequencies associated to the flow, as well as its volume-averaged properties. It is however unable to detect strange attractors close to regular solutions in the Feigenbaum as well as Newhouse-Ruelle-Takens bifurcation scenarios. It is shown that Laskar's frequency algorithm is sufficiently accurate to identify these strange attractors and thus is an efficient tool for classification of chaotic flows in high dimensional dynamical systems. Our analysis of several chaotic solutions, obtained at different magnetic field strengths, reveals a strong robustness of the main frequency of the flow. This frequency is associated to an azimuthal drift and it is very close to the frequency of the underlying unstable rotating wave. In contrast, the main frequency of volume-averaged properties can vary almost one order of magnitude as the magnetic forcing is decreased. We conclude that, at the moderate differential rotation considered, unstable rotating waves provide a good description of the variation of the main time scale of any flow with respective variations in the magnetic field.Comment: 12 pages, 9 figures and 2 tables. Accepted for Physica D: Nonlinear Phenomen